Problem: Simplify the following expression: $r = \dfrac{k}{7} - \dfrac{k}{5}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7$ and $5$ $\lcm(7, 5) = 35$ $ r = \dfrac{5}{5} \cdot \dfrac{k}{7} - \dfrac{7}{7} \cdot \dfrac{k}{5} $ $r = \dfrac{5k}{35} - \dfrac{7k}{35}$ $r = \dfrac{5k -7k}{35}$ $r = \dfrac{-2k}{35}$